Question

I am a number between $20$ and $30$. If you divide $47$ and $92$ by me, the remainders are $3$ and $4$,respectively. Which number am I?

Answer 1

Step $1$;Here reminder are $3$ and $4$

$\Rightarrow$ $47-3=$$44$ and $92-4=88$

So ,if we divide $44$ and $88$ by required number it will be completely divisible by that number.

Step $2$; Prime factorization of $44$ and $88$ are given below,

$$\begin{gathered} 44=2\times 2\times 11 \\ 88=2\times 2\times 2\times 11 \end{gathered}$$

Common factors are $2$and $11$
Therefore HCF $=2\times 11=22$
Hence, answer is $22$